0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_vampire %s %d 0.13/0.34 % Computer : n002.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Jul 13 15:36:03 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.34 This is a THF_ problem 0.13/0.34 Running vampire --ignore_missing on --mode casc_hol --cores 0 -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 Running in auto input_syntax mode. Trying TPTP 0.20/0.51 % (6360)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=lazy_gen:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_30 on theBenchmark 0.20/0.51 % (6362)lrs+1002_1_add=large:csup=on:inj=on:fe=off:chr=on:cases=on:cnfonf=eager:afr=on:afp=1000:afq=1.1:amm=sco:anc=none:er=known:fsr=off:gs=on:gsem=off:lma=on:nm=2:newcnf=on:nwc=2:stl=30:sd=1:ss=axioms:st=5.0:sp=reverse_arity:updr=off:thsq=on_50 on theBenchmark 0.20/0.52 % (6352)lrs+1010_3_av=off:fsr=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gs=on:gsem=off:nm=2:newcnf=on:nwc=2:stl=30:sp=reverse_arity:urr=on:updr=off:thsq=on_9 on theBenchmark 0.20/0.53 % (6368)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:cases=on:cnfonf=eager:afq=1.0:fde=all:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on:thsq=on_50 on theBenchmark 0.20/0.53 % (6345)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_3 on theBenchmark 0.20/0.53 % (6342)dis+10_128_acc=on:add=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on:thsq=on_2 on theBenchmark 0.20/0.53 % (6341)lrs+1011_8_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_3 on theBenchmark 0.20/0.53 % (6350)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on:thsq=on_2 on theBenchmark 0.20/0.53 % (6351)dis+1002_6_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=2.0:bsr=on:cond=on:irw=on:lma=on:nm=2:nwc=2.5:nicw=on:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark 0.20/0.53 % (6361)dis+10_4_av=off:bsr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on:thsq=on_8 on theBenchmark 0.20/0.54 % (6339)ott+1002_2_av=off:bd=preordered:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:irw=on:lma=on:nm=64:nwc=10:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark 0.20/0.55 % (6366)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:cases=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_186 on theBenchmark 0.20/0.55 % (6365)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:anc=none:bd=off:cond=on:gs=on:gsem=off:nm=64:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:updr=off:thsq=on_300 on theBenchmark 0.20/0.55 % (6343)lrs+1010_8_add=off:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on:thsq=on_13 on theBenchmark 0.20/0.56 % (6354)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=off:anc=none:gsp=input_only:gs=on:gsem=off:irw=on:lcm=predicate:nm=32:nwc=1.5:sos=on:sp=reverse_arity:thsq=on_7 on theBenchmark 0.20/0.56 % (6344)ott+1002_8:1_add=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=100000:afq=1.1:amm=off:anc=none:bd=off:bs=unit_only:fsr=off:gs=on:gsem=off:nm=32:nwc=10:sp=occurrence:urr=on:updr=off:thsq=on_14 on theBenchmark 0.20/0.56 % (6364)lrs+1010_8_add=off:afp=100000:csup=on:inj=off:cases=on:chr=off:e2e=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on:thsq=on_13 on theBenchmark 0.20/0.56 % (6340)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_2 on theBenchmark 0.20/0.57 % (6346)lrs+4_3_av=off:br=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on:thsq=on_32 on theBenchmark 0.20/0.57 % (6357)ott+11_20_afr=on:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=sco:anc=all:bsr=on:irw=on:lma=on:nm=4:nwc=1.2:sac=on:sp=occurrence:thsq=on_6 on theBenchmark 0.20/0.57 % (6356)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_30 on theBenchmark 0.20/0.57 % (6367)dis+1002_4_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=1.0:anc=none:cond=fast:fde=none:gs=on:gsaa=full_model:lma=on:lwlo=on:nm=0:nwc=1.5:sp=reverse_arity:tha=off_300 on theBenchmark 0.20/0.57 % (6353)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:fsr=off:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1:stl=30:sd=3:ss=axioms:st=1.5:sos=on:thsq=on_1 on theBenchmark 0.20/0.57 % (6349)dis+10_128_acc=on:add=off:add=off:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on:thsq=on_40 on theBenchmark 0.20/0.57 % (6348)dis+1_2:3_acc=on:add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=2.0:amm=sco:anc=none:er=filter:fsr=off:gsp=input_only:gs=on:gsem=off:nm=64:newcnf=on:nwc=1:thsq=on_3 on theBenchmark 0.20/0.57 % (6358)dis+1002_3:1_acc=model:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=40000:afq=1.1:anc=none:ccuc=first:fsr=off:gsp=input_only:irw=on:nm=16:nwc=1:sos=all:thsq=on_8 on theBenchmark 0.20/0.58 % (6363)lrs+1011_5_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=1000:afq=1.2:anc=none:fsr=off:irw=on:lma=on:nm=64:newcnf=on:nwc=1:stl=30:sd=3:ss=axioms:st=2.0:sos=on:sac=on:sp=reverse_arity:urr=on:updr=off:thsq=on_130 on theBenchmark 0.20/0.58 % (6359)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.4:amm=sco:anc=none:cond=on:lma=on:nm=64:nwc=1.3:stl=30:sac=on:urr=on:thsq=on_41 on theBenchmark 0.20/0.58 % (6347)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark 0.20/0.59 % (6355)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:anc=none:gsp=input_only:irw=on:lwlo=on:nm=2:newcnf=on:nwc=1.7:sac=on:sp=occurrence:thsq=on_300 on theBenchmark 4.97/1.12 % (6355)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.26/1.33 % (6345)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.26/1.34 % (6343)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.85/1.35 % (6356)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.85/1.35 % (6346)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.85/1.35 % (6348)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.85/1.36 % (6364)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 7.70/1.45 % (6362)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 7.70/1.45 % (6341)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 7.80/1.46 % (6355)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 7.80/1.47 % (6347)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 7.80/1.47 % (6363)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 7.80/1.49 % (6352)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 8.27/1.53 % (6341)Time limit reached! 8.27/1.53 % (6341)------------------------------ 8.27/1.53 % (6341)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 8.27/1.53 % (6341)Termination reason: Time limit 8.27/1.53 8.27/1.53 % (6341)Memory used [KB]: 16630 8.27/1.53 % (6341)Time elapsed: 1.033 s 8.27/1.53 % (6341)------------------------------ 8.27/1.53 % (6341)------------------------------ 8.56/1.58 % (6369)dis+1011_10_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence:thsq=on_75 on theBenchmark 8.56/1.59 % (6353)Time limit reached! 8.56/1.59 % (6353)------------------------------ 8.56/1.59 % (6353)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 8.56/1.59 % (6353)Termination reason: Time limit 8.56/1.59 8.56/1.59 % (6353)Memory used [KB]: 12153 8.56/1.59 % (6353)Time elapsed: 1.093 s 8.56/1.59 % (6353)------------------------------ 8.56/1.59 % (6353)------------------------------ 9.20/1.64 % (6370)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:cases=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark 10.09/1.76 % (6345)Time limit reached! 10.09/1.76 % (6345)------------------------------ 10.09/1.76 % (6345)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 10.09/1.76 % (6345)Termination reason: Time limit 10.09/1.76 10.09/1.76 % (6345)Memory used [KB]: 15735 10.09/1.76 % (6345)Time elapsed: 1.261 s 10.09/1.76 % (6345)------------------------------ 10.09/1.76 % (6345)------------------------------ 10.09/1.77 % (6342)Time limit reached! 10.09/1.77 % (6342)------------------------------ 10.09/1.77 % (6342)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 10.09/1.77 % (6342)Termination reason: Time limit 10.09/1.77 10.09/1.77 % (6342)Memory used [KB]: 16247 10.09/1.77 % (6342)Time elapsed: 1.263 s 10.09/1.77 % (6342)------------------------------ 10.09/1.77 % (6342)------------------------------ 10.09/1.83 % (6371)lrs+1011_8_add=large:csup=on:inj=on:prag=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_26 on theBenchmark 10.09/1.83 % (6372)lrs+1011_8_add=large:csup=on:fe=off:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_30 on theBenchmark 10.71/1.86 % (6361)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 11.21/1.90 % (6354)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 11.21/1.90 % (6348)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 11.21/1.92 % (6358)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 12.98/2.12 % (6365)First to succeed. 13.62/2.23 % (6365)Refutation found. Thanks to Tanya! 13.62/2.23 % SZS status Theorem for theBenchmark 13.62/2.23 % SZS output start Proof for theBenchmark 13.62/2.23 thf(type_def_6, type, >: ($tType * $tType) > $tType). 13.62/2.23 thf(func_def_7, type, c_Eps_i: ($i > $o) > $i). 13.62/2.23 thf(func_def_10, type, c_not: $o > $o). 13.62/2.23 thf(func_def_11, type, c_and: $o > $o > $o). 13.62/2.23 thf(func_def_12, type, c_or: $o > $o > $o). 13.62/2.23 thf(func_def_13, type, c_iff: $o > $o > $o). 13.62/2.23 thf(func_def_14, type, c_In: $i > $i > $o). 13.62/2.23 thf(func_def_15, type, c_Subq: $i > $i > $o). 13.62/2.23 thf(func_def_17, type, c_Union: $i > $i). 13.62/2.23 thf(func_def_18, type, c_Power: $i > $i). 13.62/2.23 thf(func_def_19, type, c_Repl: $i > ($i > $i) > $i). 13.62/2.23 thf(func_def_20, type, c_TransSet: $i > $o). 13.62/2.23 thf(func_def_21, type, c_atleast2: $i > $o). 13.62/2.23 thf(func_def_22, type, c_atleast3: $i > $o). 13.62/2.23 thf(func_def_23, type, c_atleast4: $i > $o). 13.62/2.23 thf(func_def_24, type, c_atleast5: $i > $o). 13.62/2.23 thf(func_def_25, type, c_atleast6: $i > $o). 13.62/2.23 thf(func_def_26, type, c_exactly2: $i > $o). 13.62/2.23 thf(func_def_27, type, c_exactly3: $i > $o). 13.62/2.23 thf(func_def_28, type, c_exactly4: $i > $o). 13.62/2.23 thf(func_def_29, type, c_exactly5: $i > $o). 13.62/2.23 thf(func_def_30, type, c_exu_i: ($i > $o) > $o). 13.62/2.23 thf(func_def_31, type, c_reflexive_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_32, type, c_irreflexive_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_33, type, c_symmetric_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_34, type, c_antisymmetric_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_35, type, c_transitive_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_36, type, c_eqreln_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_37, type, c_per_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_38, type, c_linear_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_39, type, c_trichotomous_or_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_40, type, c_partialorder_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_41, type, c_totalorder_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_42, type, c_strictpartialorder_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_43, type, c_stricttotalorder_i: ($i > $i > $o) > $o). 13.62/2.23 thf(func_def_44, type, c_If_i: $o > $i > $i > $i). 13.62/2.23 thf(func_def_45, type, c_exactly1of2: $o > $o > $o). 13.62/2.23 thf(func_def_46, type, c_exactly1of3: $o > $o > $o > $o). 13.62/2.23 thf(func_def_47, type, c_nIn: $i > $i > $o). 13.62/2.23 thf(func_def_48, type, c_nSubq: $i > $i > $o). 13.62/2.23 thf(func_def_49, type, c_UPair: $i > $i > $i). 13.62/2.23 thf(func_def_50, type, c_Sing: $i > $i). 13.62/2.23 thf(func_def_51, type, c_binunion: $i > $i > $i). 13.62/2.23 thf(func_def_52, type, c_SetAdjoin: $i > $i > $i). 13.62/2.23 thf(func_def_53, type, c_famunion: $i > ($i > $i) > $i). 13.62/2.23 thf(func_def_54, type, c_Sep: $i > ($i > $o) > $i). 13.62/2.23 thf(func_def_55, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 13.62/2.23 thf(func_def_56, type, c_binintersect: $i > $i > $i). 13.62/2.23 thf(func_def_57, type, c_setminus: $i > $i > $i). 13.62/2.23 thf(func_def_58, type, c_inj: $i > $i > ($i > $i) > $o). 13.62/2.23 thf(func_def_59, type, c_bij: $i > $i > ($i > $i) > $o). 13.62/2.23 thf(func_def_60, type, c_atleastp: $i > $i > $o). 13.62/2.23 thf(func_def_61, type, c_equip: $i > $i > $o). 13.62/2.23 thf(func_def_62, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o). 13.62/2.23 thf(func_def_63, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i). 13.62/2.23 thf(func_def_64, type, c_ordsucc: $i > $i). 13.62/2.23 thf(func_def_65, type, c_nat_p: $i > $o). 13.62/2.23 thf(func_def_66, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i). 13.62/2.23 thf(func_def_67, type, c_add_nat: $i > $i > $i). 13.62/2.23 thf(func_def_68, type, c_mul_nat: $i > $i > $i). 13.62/2.23 thf(func_def_69, type, c_ordinal: $i > $o). 13.62/2.23 thf(func_def_70, type, c_V_: $i > $i). 13.62/2.23 thf(func_def_71, type, c_Inj1: $i > $i). 13.62/2.23 thf(func_def_72, type, c_Inj0: $i > $i). 13.62/2.23 thf(func_def_73, type, c_Unj: $i > $i). 13.62/2.23 thf(func_def_74, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i). 13.62/2.23 thf(func_def_75, type, c_setsum: $i > $i > $i). 13.62/2.23 thf(func_def_76, type, c_proj0: $i > $i). 13.62/2.23 thf(func_def_77, type, c_proj1: $i > $i). 13.62/2.23 thf(func_def_78, type, c_binrep: $i > $i > $i). 13.62/2.23 thf(func_def_79, type, c_lam: $i > ($i > $i) > $i). 13.62/2.23 thf(func_def_80, type, c_setprod: $i > $i > $i). 13.62/2.23 thf(func_def_81, type, c_ap: $i > $i > $i). 13.62/2.23 thf(func_def_82, type, c_setsum_p: $i > $o). 13.62/2.23 thf(func_def_83, type, c_tuple_p: $i > $i > $o). 13.62/2.23 thf(func_def_84, type, c_Pi: $i > ($i > $i) > $i). 13.62/2.23 thf(func_def_85, type, c_setexp: $i > $i > $i). 13.62/2.23 thf(func_def_86, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i). 13.62/2.23 thf(func_def_87, type, c_set_of_pairs: $i > $o). 13.62/2.23 thf(func_def_88, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i). 13.62/2.23 thf(func_def_89, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o). 13.62/2.23 thf(func_def_90, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o). 13.62/2.23 thf(func_def_91, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o). 13.62/2.23 thf(func_def_92, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o). 13.62/2.23 thf(func_def_93, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o). 13.62/2.23 thf(func_def_94, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o). 13.62/2.23 thf(func_def_95, type, c_SNoElts_: $i > $i). 13.62/2.23 thf(func_def_96, type, c_SNo_: $i > $i > $o). 13.62/2.23 thf(func_def_97, type, c_PSNo: $i > ($i > $o) > $i). 13.62/2.23 thf(func_def_98, type, c_SNo: $i > $o). 13.62/2.23 thf(func_def_99, type, c_SNoLev: $i > $i). 13.62/2.23 thf(func_def_100, type, c_SNoEq_: $i > $i > $i > $o). 13.62/2.23 thf(func_def_101, type, c_SNoLt: $i > $i > $o). 13.62/2.23 thf(func_def_102, type, c_SNoLe: $i > $i > $o). 13.62/2.23 thf(func_def_103, type, c_binop_on: $i > ($i > $i > $i) > $o). 13.62/2.23 thf(func_def_104, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o). 13.62/2.23 thf(func_def_105, type, c_Loop_with_defs: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 13.62/2.23 thf(func_def_106, type, c_Loop_with_defs_cex1: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 13.62/2.23 thf(func_def_107, type, c_Loop_with_defs_cex2: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 13.62/2.23 thf(func_def_108, type, c_combinator: $i > $o). 13.62/2.23 thf(func_def_109, type, c_combinator_equiv: $i > $i > $o). 13.62/2.23 thf(func_def_110, type, c_equip_mod: $i > $i > $i > $o). 13.62/2.23 thf(func_def_112, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)). 13.62/2.23 thf(func_def_115, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)). 13.62/2.23 thf(func_def_116, type, iCOMB: !>[X0: $tType]:(X0 > X0)). 13.62/2.23 thf(func_def_117, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)). 13.62/2.23 thf(func_def_118, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)). 13.62/2.23 thf(func_def_119, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)). 13.62/2.23 thf(func_def_120, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)). 13.62/2.23 thf(func_def_121, type, vIMP: $o > $o > $o). 13.62/2.23 thf(func_def_122, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)). 13.62/2.23 thf(func_def_123, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)). 13.62/2.23 thf(func_def_124, type, sK0: (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i). 13.62/2.23 thf(func_def_125, type, sK1: ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i). 13.62/2.23 thf(func_def_126, type, sK2: ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i). 13.62/2.23 thf(func_def_127, type, sK3: (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i). 13.62/2.23 thf(func_def_128, type, sK4: ($i > $o) > $i). 13.62/2.23 thf(func_def_129, type, sK5: ($i > $o) > $i > $i). 13.62/2.23 thf(func_def_130, type, sK6: ($i > $o) > $i). 13.62/2.23 thf(func_def_131, type, sK7: ($i > $o) > $i). 13.62/2.23 thf(func_def_132, type, sK8: ($i > $o) > $i). 13.62/2.23 thf(func_def_133, type, sK9: ($i > $o) > $i). 13.62/2.23 thf(func_def_134, type, sK10: ($i > $o) > $i). 13.62/2.23 thf(func_def_136, type, vAND: $o > $o > $o). 13.62/2.23 thf(func_def_137, type, vOR: $o > $o > $o). 13.62/2.23 thf(func_def_138, type, vNOT: $o > $o). 13.62/2.23 thf(func_def_143, type, sK13: $i > $i > $i). 13.62/2.23 thf(func_def_144, type, sK14: $i > $i > $i). 13.62/2.23 thf(func_def_145, type, sK15: $i > $i > $i > $o). 13.62/2.23 thf(func_def_146, type, sK16: ($i > $i) > $i > $i > $i). 13.62/2.23 thf(func_def_147, type, sK17: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_148, type, sK18: $i > $i > $i). 13.62/2.23 thf(func_def_149, type, sK19: $i > $i > $i). 13.62/2.23 thf(func_def_150, type, sK20: $i > $i > $i > $o). 13.62/2.23 thf(func_def_151, type, sK21: ($i > $i) > $i > $i > $i). 13.62/2.23 thf(func_def_152, type, sK22: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_153, type, sK23: $i > $i > $i). 13.62/2.23 thf(func_def_154, type, sK24: $i > $i > $i). 13.62/2.23 thf(func_def_155, type, sK25: $i > $i > $i > $o). 13.62/2.23 thf(func_def_156, type, sK26: ($i > $i) > $i > $i > $i). 13.62/2.23 thf(func_def_157, type, sK27: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_158, type, sK28: $i > $i > $i). 13.62/2.23 thf(func_def_159, type, sK29: $i > ($i > $i) > $i > $i). 13.62/2.23 thf(func_def_160, type, sK30: $i > $i > $i). 13.62/2.23 thf(func_def_161, type, sK31: $i > $i > $i). 13.62/2.23 thf(func_def_162, type, sK32: $i > $i > $i). 13.62/2.23 thf(func_def_163, type, sK33: $i > $i > $i). 13.62/2.23 thf(func_def_164, type, sK34: $i > $i > $i). 13.62/2.23 thf(func_def_165, type, sK35: $i > $i > $i). 13.62/2.23 thf(func_def_166, type, sK36: $i > $i > $i). 13.62/2.23 thf(func_def_167, type, sK37: $i > $i > $i > $o). 13.62/2.23 thf(func_def_168, type, sK38: $i > $i > $i > $o). 13.62/2.23 thf(func_def_169, type, sK39: $i > $i > $i > $o). 13.62/2.23 thf(func_def_170, type, sK40: $i > $i > $i > $o). 13.62/2.23 thf(func_def_171, type, sK41: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_172, type, sK42: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_173, type, sK43: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_174, type, sK44: $i > ($i > $i) > $i > $i > $o). 13.62/2.23 thf(func_def_175, type, sK45: ($i > $i) > $i > $i > $i). 13.62/2.23 thf(func_def_176, type, sK46: ($i > $i) > $i > $i > $i). 13.62/2.23 thf(func_def_177, type, sK47: $i > ($i > $i) > $i > $i). 13.62/2.23 thf(func_def_181, type, sK51: $o > $o > $o). 13.62/2.23 thf(func_def_182, type, sK52: $o > $o > $o). 13.62/2.23 thf(func_def_183, type, sK53: $i > $i > $i > $o). 13.62/2.23 thf(func_def_184, type, sK54: $i > $i > $i > $o). 13.62/2.23 thf(func_def_185, type, sK55: $i > ($i > $i) > $i > $i > $o). 13.62/2.23 thf(func_def_186, type, sK56: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_187, type, sK57: $i > $i > $i). 13.62/2.23 thf(func_def_188, type, sK58: $i > $i > $i). 13.62/2.23 thf(func_def_189, type, sK59: $i > $i > $i). 13.62/2.23 thf(func_def_190, type, sK60: $i > $i > $i). 13.62/2.23 thf(func_def_191, type, sK61: $i > $i > $i). 13.62/2.23 thf(func_def_192, type, sK62: $i > $i > $i). 13.62/2.23 thf(func_def_193, type, sK63: $i > $i > $i). 13.62/2.23 thf(func_def_194, type, sK64: $i > $i > $i). 13.62/2.23 thf(func_def_195, type, sK65: $o > $o > $o). 13.62/2.23 thf(func_def_196, type, sK66: $o > $o > $o). 13.62/2.23 thf(func_def_204, type, sK74: $i > $i). 13.62/2.23 thf(func_def_205, type, sK75: $i > $i). 13.62/2.23 thf(func_def_206, type, sK76: $i > $i > $o). 13.62/2.23 thf(func_def_207, type, sK77: $i > $i > $i). 13.62/2.23 thf(func_def_208, type, sK78: $i > ($i > $i) > $i > $i). 13.62/2.23 thf(func_def_209, type, sK79: $i > $i > $i). 13.62/2.23 thf(func_def_210, type, sK80: $i > $i > $i). 13.62/2.23 thf(func_def_211, type, sK81: $i > $i > $i > $o). 13.62/2.23 thf(func_def_212, type, sK82: $i > $i > ($i > $i) > $i > $o). 13.62/2.23 thf(func_def_213, type, sK83: ($i > $i) > $i > $i > $i). 13.62/2.23 thf(func_def_215, type, sK85: $o > $o > $o). 13.62/2.23 thf(func_def_216, type, sK86: $o > $o > $o). 13.62/2.23 thf(func_def_217, type, sK87: $i > $i > $i). 13.62/2.23 thf(func_def_218, type, sK88: $i > $i > $i). 13.62/2.23 thf(f3522,plain,( 13.62/2.23 $false), 13.62/2.23 inference(avatar_sat_refutation,[],[f1854,f2830,f3521])). 13.62/2.23 thf(f3521,plain,( 13.62/2.23 ~spl11_1), 13.62/2.23 inference(avatar_contradiction_clause,[],[f3520])). 13.62/2.23 thf(f3520,plain,( 13.62/2.23 $false | ~spl11_1), 13.62/2.23 inference(trivial_inequality_removal,[],[f3519])). 13.62/2.23 thf(f3519,plain,( 13.62/2.23 ($true = $false) | ~spl11_1), 13.62/2.23 inference(combinator_demodulation,[],[f2943])). 13.62/2.23 thf(f2943,plain,( 13.62/2.23 ( ! [X0 : $tType,X1 : X0] : (($true = ((kCOMB @ $false) @ X1))) ) | ~spl11_1), 13.62/2.23 inference(primitive_instantiation,[],[f1843])). 13.62/2.23 thf(f1843,plain,( 13.62/2.23 ( ! [X2 : $o] : (($true = X2)) ) | ~spl11_1), 13.62/2.23 inference(avatar_component_clause,[],[f1842])). 13.62/2.23 thf(f1842,plain,( 13.62/2.23 spl11_1 <=> ! [X2 : $o] : ($true = X2)), 13.62/2.23 introduced(avatar_definition,[new_symbols(naming,[spl11_1])])). 13.62/2.23 thf(f2830,plain,( 13.62/2.23 ~spl11_2), 13.62/2.23 inference(avatar_contradiction_clause,[],[f2829])). 13.62/2.23 thf(f2829,plain,( 13.62/2.23 $false | ~spl11_2), 13.62/2.23 inference(trivial_inequality_removal,[],[f2828])). 13.62/2.23 thf(f2828,plain,( 13.62/2.23 ($true = $false) | ~spl11_2), 13.62/2.23 inference(forward_demodulation,[],[f2827,f1846])). 13.62/2.23 thf(f1846,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : ((((c_In @ X1) @ X0) = $false)) ) | ~spl11_2), 13.62/2.23 inference(avatar_component_clause,[],[f1845])). 13.62/2.23 thf(f1845,plain,( 13.62/2.23 spl11_2 <=> ! [X1,X0] : (((c_In @ X1) @ X0) = $false)), 13.62/2.23 introduced(avatar_definition,[new_symbols(naming,[spl11_2])])). 13.62/2.23 thf(f2827,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = ((c_In @ X0) @ (c_Power @ X1)))) ) | ~spl11_2), 13.62/2.23 inference(trivial_inequality_removal,[],[f2826])). 13.62/2.23 thf(f2826,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) ) | ~spl11_2), 13.62/2.23 inference(forward_demodulation,[],[f2201,f1846])). 13.62/2.23 thf(f2201,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = ((c_In @ ((sK30 @ X1) @ X0)) @ X0)) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) )), 13.62/2.23 inference(duplicate_literal_removal,[],[f2200])). 13.62/2.23 thf(f2200,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = ((c_In @ ((sK30 @ X1) @ X0)) @ X0)) | ($true = ((c_In @ X0) @ (c_Power @ X1))) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f2198])). 13.62/2.23 thf(f2198,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = ((c_In @ ((sK30 @ X1) @ X0)) @ X0)) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1))))) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f2196])). 13.62/2.23 thf(f2196,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($false = ((vIMP @ ((c_In @ ((sK30 @ X1) @ X0)) @ X0)) @ ((c_In @ ((sK30 @ X1) @ X0)) @ X1))) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1))))) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) )), 13.62/2.23 inference(combinator_demodulation,[],[f2195])). 13.62/2.23 thf(f2195,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($false = (((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)) @ ((sK30 @ X1) @ X0))) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1))))) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) )), 13.62/2.23 inference(sigma_clausification,[],[f2194])). 13.62/2.23 thf(f2194,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($false = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1))))) | ($true = ((c_In @ X0) @ (c_Power @ X1)))) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f2193])). 13.62/2.23 thf(f2193,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1)))) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))))) )), 13.62/2.23 inference(condensation,[],[f2192])). 13.62/2.23 thf(f2192,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1)))) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1))))) | ($true = X2)) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f2190])). 13.62/2.23 thf(f2190,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1)))) @ X2)) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1))))) | ($true = X2)) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f2189])). 13.62/2.23 thf(f2189,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((vIMP @ ((vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1)))) @ X2)) @ X2)) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))))) )), 13.62/2.23 inference(boolean_simplification,[],[f2188])). 13.62/2.23 thf(f2188,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((vIMP @ ((vIMP @ $true) @ ((vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1)))) @ X2))) @ X2)) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))))) )), 13.62/2.23 inference(combinator_demodulation,[],[f2187])). 13.62/2.23 thf(f2187,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ $true)) @ (vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1))))))) @ iCOMB) @ X2)) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))))) )), 13.62/2.23 inference(pi_clausification,[],[f1883])). 13.62/2.23 thf(f1883,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ $true)) @ (vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ (c_Power @ X1))))))) @ iCOMB))) | ($false = ((vIMP @ ((c_In @ X0) @ (c_Power @ X1))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))))) )), 13.62/2.23 inference(superposition,[],[f407,f755])). 13.62/2.23 thf(f755,plain,( 13.62/2.23 ( ! [X3 : $o] : (($true = X3) | ($false = X3)) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f739])). 13.62/2.23 thf(f739,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i > $i] : (($false = ((vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))) @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ X3)) | ($true = X3)) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f738])). 13.62/2.23 thf(f738,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i > $i] : (($false = ((vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2))))) @ ((vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))) @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ X3))) | ($true = X3)) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f737])). 13.62/2.23 thf(f737,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i > $i] : (($true = ((vIMP @ ((vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2))))) @ ((vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))) @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ X3))) @ X3))) )), 13.62/2.23 inference(combinator_demodulation,[],[f736])). 13.62/2.23 thf(f736,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i > $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))))) @ (vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))) @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ iCOMB) @ X3))) )), 13.62/2.23 inference(pi_clausification,[],[f467])). 13.62/2.23 thf(f467,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))))) @ (vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))) @ ((c_In @ X2) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ iCOMB)))) )), 13.62/2.23 inference(superposition,[],[f405,f320])). 13.62/2.23 thf(f320,plain,( 13.62/2.23 ( ! [X4 : $i] : ((((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X4)) )), 13.62/2.23 inference(cnf_transformation,[],[f301])). 13.62/2.23 thf(f301,plain,( 13.62/2.23 (c_False != $true) & ! [X4] : (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X4) & (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) & ! [X5 : $i > ($i > $i > $i) > $i > $i,X6,X7,X8 : (($i > $i > $i) > $i > $i) > $i] : (((sK1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ sK1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((sK2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X6) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((sK2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((sK1 @ (kCOMB @ ((bCOMB @ X8) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((sK3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((sK3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X6) @ ((sK1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((sK1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X6))) @ ((c_setsum @ ((c_setsum @ X7) @ (((((sK2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X8 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X5 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X5 @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (sK1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X6)))) & ! [X9,X10 : (($i > $i) > $i > $i) > $i,X11] : (((sK1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X10 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X9) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X11) @ (c_Inj1 @ X11))))) @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X10 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((sK3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) & ! [X12 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X13 : (($i > $i > $i) > $i > $i) > $i,X14 : $i > $i] : ((X14 @ (c_Inj0 @ c_Empty)) = (((((sK2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (sK2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X14 @ c_Empty))) @ (X13 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((sK2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((sK3 @ (kCOMB @ (X13 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X14 @ c_Empty)) @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X14 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X14 @ (c_Inj1 @ c_Empty)))) & ! [X15,X16 : $i > $i] : ((((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (sK2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X16)) @ iCOMB)))) @ kCOMB)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((sK2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X16 @ c_Empty))) @ c_Empty)) @ X15) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X16 @ c_Empty))) = X15) & ! [X17,X18 : $i > $i] : (((sK3 @ (kCOMB @ c_Empty)) @ X18) = (X18 @ ((c_setsum @ (((((sK2 @ (kCOMB @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X17) @ c_Empty) @ c_Empty)) @ ((sK1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) & ! [X19 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X20 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((sK3 @ (kCOMB @ ((c_setsum @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((sK2 @ (kCOMB @ (kCOMB @ ((((X20 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X19 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB))), 13.62/2.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f299,f300])). 13.62/2.23 thf(f300,plain,( 13.62/2.23 ? [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : ((c_False != $true) & ! [X4] : (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X4) & (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ X2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) & ! [X5 : $i > ($i > $i > $i) > $i > $i,X6,X7,X8 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ X1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X6) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ ((bCOMB @ X8) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((X3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((X3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X6) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X6))) @ ((c_setsum @ ((c_setsum @ X7) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X8 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X5 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X5 @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (X1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X6)))) & ! [X9,X10 : (($i > $i) > $i > $i) > $i,X11] : (((X1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X10 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X9) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X11) @ (c_Inj1 @ X11))))) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X10 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) & ! [X12 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X13 : (($i > $i > $i) > $i > $i) > $i,X14 : $i > $i] : ((X14 @ (c_Inj0 @ c_Empty)) = (((((X2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X14 @ c_Empty))) @ (X13 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((X2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((X3 @ (kCOMB @ (X13 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X14 @ c_Empty)) @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X14 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X14 @ (c_Inj1 @ c_Empty)))) & ! [X15,X16 : $i > $i] : ((((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X16)) @ iCOMB)))) @ kCOMB)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X16 @ c_Empty))) @ c_Empty)) @ X15) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X16 @ c_Empty))) = X15) & ! [X17,X18 : $i > $i] : (((X3 @ (kCOMB @ c_Empty)) @ X18) = (X18 @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X17) @ c_Empty) @ c_Empty)) @ ((X1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) & ! [X19 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X20 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ ((((X20 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X19 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB))) => ((c_False != $true) & ! [X4] : (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X4) & (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) & ! [X8 : (($i > $i > $i) > $i > $i) > $i,X7,X6,X5 : $i > ($i > $i > $i) > $i > $i] : (((sK1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ sK1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((sK2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X6) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((sK2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((sK1 @ (kCOMB @ ((bCOMB @ X8) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((sK3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((sK3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X6) @ ((sK1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((sK1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X6))) @ ((c_setsum @ ((c_setsum @ X7) @ (((((sK2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X8 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X5 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X5 @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (sK1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X6)))) & ! [X11,X10 : (($i > $i) > $i > $i) > $i,X9] : (((sK1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X10 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X9) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X11) @ (c_Inj1 @ X11))))) @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X10 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((sK3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) & ! [X14 : $i > $i,X13 : (($i > $i > $i) > $i > $i) > $i,X12 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i] : ((X14 @ (c_Inj0 @ c_Empty)) = (((((sK2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (sK2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X14 @ c_Empty))) @ (X13 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((sK2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((sK3 @ (kCOMB @ (X13 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X14 @ c_Empty)) @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X14 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X14 @ (c_Inj1 @ c_Empty)))) & ! [X16 : $i > $i,X15] : ((((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (sK2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X16)) @ iCOMB)))) @ kCOMB)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((sK2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X16 @ c_Empty))) @ c_Empty)) @ X15) @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X16 @ c_Empty))) = X15) & ! [X18 : $i > $i,X17] : (((sK3 @ (kCOMB @ c_Empty)) @ X18) = (X18 @ ((c_setsum @ (((((sK2 @ (kCOMB @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X17) @ c_Empty) @ c_Empty)) @ ((sK1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) & ! [X20 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i,X19 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i] : ((c_Inj1 @ c_Empty) = ((sK3 @ (kCOMB @ ((c_setsum @ ((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((sK1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((sK2 @ (kCOMB @ (kCOMB @ ((((X20 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X19 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((sK1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB)))), 13.62/2.23 introduced(choice_axiom,[])). 13.62/2.23 thf(f299,plain,( 13.62/2.23 ? [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : ((c_False != $true) & ! [X4] : (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X4) & (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ X2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) & ! [X5 : $i > ($i > $i > $i) > $i > $i,X6,X7,X8 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ X1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X6) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ ((bCOMB @ X8) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((X3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((X3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X6) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X6))) @ ((c_setsum @ ((c_setsum @ X7) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X8 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X5 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X5 @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (X1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X6)))) & ! [X9,X10 : (($i > $i) > $i > $i) > $i,X11] : (((X1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X10 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X9) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X11) @ (c_Inj1 @ X11))))) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X10 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) & ! [X12 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X13 : (($i > $i > $i) > $i > $i) > $i,X14 : $i > $i] : ((X14 @ (c_Inj0 @ c_Empty)) = (((((X2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X14 @ c_Empty))) @ (X13 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((X2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((X3 @ (kCOMB @ (X13 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X14 @ c_Empty)) @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X14 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X12 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X14 @ (c_Inj1 @ c_Empty)))) & ! [X15,X16 : $i > $i] : ((((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X16)) @ iCOMB)))) @ kCOMB)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X16 @ c_Empty))) @ c_Empty)) @ X15) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X16 @ c_Empty))) = X15) & ! [X17,X18 : $i > $i] : (((X3 @ (kCOMB @ c_Empty)) @ X18) = (X18 @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X17) @ c_Empty) @ c_Empty)) @ ((X1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) & ! [X19 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X20 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ ((((X20 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X19 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB)))), 13.62/2.23 inference(rectify,[],[f291])). 13.62/2.23 thf(f291,plain,( 13.62/2.23 ? [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : ((c_False != $true) & ! [X20] : (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X20) & (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ X2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) & ! [X16 : $i > ($i > $i > $i) > $i > $i,X17,X18,X19 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ X1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X17) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ ((bCOMB @ X19) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((X3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((X3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X17) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X17))) @ ((c_setsum @ ((c_setsum @ X18) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X19 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X16 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X16 @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (X1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X17)))) & ! [X13,X14 : (($i > $i) > $i > $i) > $i,X15] : (((X1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X14 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X13) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X15) @ (c_Inj1 @ X15))))) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X14 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) & ! [X10 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X11 : (($i > $i > $i) > $i > $i) > $i,X12 : $i > $i] : ((X12 @ (c_Inj0 @ c_Empty)) = (((((X2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X12 @ c_Empty))) @ (X11 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((X2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((X3 @ (kCOMB @ (X11 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X12 @ c_Empty)) @ c_Empty) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X12 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X12 @ (c_Inj1 @ c_Empty)))) & ! [X8,X9 : $i > $i] : ((((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X9)) @ iCOMB)))) @ kCOMB)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X9 @ c_Empty))) @ c_Empty)) @ X8) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X9 @ c_Empty))) = X8) & ! [X6,X7 : $i > $i] : (((X3 @ (kCOMB @ c_Empty)) @ X7) = (X7 @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X6) @ c_Empty) @ c_Empty)) @ ((X1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) & ! [X4 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X5 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ ((((X5 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X4 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB)))), 13.62/2.23 inference(flattening,[],[f290])). 13.62/2.23 thf(f290,plain,( 13.62/2.23 ? [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : (((((((((c_False != $true) & ! [X20] : (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X20)) & (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ X2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) & ! [X16 : $i > ($i > $i > $i) > $i > $i,X17,X18,X19 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ X1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X17) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ ((bCOMB @ X19) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((X3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((X3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X17) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X17))) @ ((c_setsum @ ((c_setsum @ X18) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X19 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X16 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X16 @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (X1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X17))))) & ! [X13,X14 : (($i > $i) > $i > $i) > $i,X15] : (((X1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X14 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X13) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X15) @ (c_Inj1 @ X15))))) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X14 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty)))))) & ! [X10 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X11 : (($i > $i > $i) > $i > $i) > $i,X12 : $i > $i] : ((X12 @ (c_Inj0 @ c_Empty)) = (((((X2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X12 @ c_Empty))) @ (X11 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((X2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((X3 @ (kCOMB @ (X11 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X12 @ c_Empty)) @ c_Empty) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X12 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X12 @ (c_Inj1 @ c_Empty))))) & ! [X8,X9 : $i > $i] : ((((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X9)) @ iCOMB)))) @ kCOMB)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X9 @ c_Empty))) @ c_Empty)) @ X8) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X9 @ c_Empty))) = X8)) & ! [X6,X7 : $i > $i] : (((X3 @ (kCOMB @ c_Empty)) @ X7) = (X7 @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X6) @ c_Empty) @ c_Empty)) @ ((X1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty))))) & ! [X4 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X5 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ ((((X5 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X4 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB)))), 13.62/2.23 inference(ennf_transformation,[],[f288])). 13.62/2.23 thf(f288,plain,( 13.62/2.23 ~! [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : (! [X4 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X5 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ ((((X5 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X4 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB)) => (! [X6,X7 : $i > $i] : (((X3 @ (kCOMB @ c_Empty)) @ X7) = (X7 @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X6) @ c_Empty) @ c_Empty)) @ ((X1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) => (! [X8,X9 : $i > $i] : ((((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X9)) @ iCOMB)))) @ kCOMB)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X9 @ c_Empty))) @ c_Empty)) @ X8) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X9 @ c_Empty))) = X8) => (! [X10 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X11 : (($i > $i > $i) > $i > $i) > $i,X12 : $i > $i] : ((X12 @ (c_Inj0 @ c_Empty)) = (((((X2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X12 @ c_Empty))) @ (X11 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((X2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((X3 @ (kCOMB @ (X11 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X12 @ c_Empty)) @ c_Empty) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X12 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X10 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X12 @ (c_Inj1 @ c_Empty)))) => (! [X13,X14 : (($i > $i) > $i > $i) > $i,X15] : (((X1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X14 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X13) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X15) @ (c_Inj1 @ X15))))) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X14 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) => (! [X16 : $i > ($i > $i > $i) > $i > $i,X17,X18,X19 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ X1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X17) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ ((bCOMB @ X19) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((X3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((X3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X17) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X17))) @ ((c_setsum @ ((c_setsum @ X18) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X19 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X16 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X16 @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (X1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X17)))) => ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ X2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) => (! [X20] : (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X20) => (c_False = $true)))))))))), 13.62/2.23 inference(rectify,[],[f113])). 13.62/2.23 thf(f113,plain,( 13.62/2.23 ~! [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : (! [X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X7 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ ((((X7 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty)))) @ (kCOMB @ c_Empty)) @ ((X6 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)))))) @ iCOMB)) => (! [X32,X33 : $i > $i] : (((X3 @ (kCOMB @ c_Empty)) @ X33) = (X33 @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ iCOMB) @ X32) @ c_Empty) @ c_Empty)) @ ((X1 @ ((cCOMB @ ((bCOMB @ cCOMB) @ (cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))) @ c_Empty)))) => (! [X49,X52 : $i > $i] : ((((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ ((sCOMB @ ((bCOMB @ (((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ X52)) @ iCOMB)))) @ kCOMB)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ (X52 @ c_Empty))) @ c_Empty)) @ X49) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))))) @ ((c_setsum @ c_Empty) @ (X52 @ c_Empty))) = X49) => (! [X102 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X103 : (($i > $i > $i) > $i > $i) > $i,X104 : $i > $i] : ((X104 @ (c_Inj0 @ c_Empty)) = (((((X2 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ ((bCOMB @ (X2 @ (kCOMB @ (kCOMB @ c_Empty)))) @ kCOMB)) @ (X104 @ c_Empty))) @ (X103 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))))) @ c_Empty))) @ (kCOMB @ c_Empty)) @ ((((X102 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty) @ (((((X2 @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (kCOMB @ ((X3 @ (kCOMB @ (X103 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ (X104 @ c_Empty)) @ c_Empty) @ ((((X102 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X104 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X102 @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X104 @ (c_Inj1 @ c_Empty)))) => (! [X138,X140 : (($i > $i) > $i > $i) > $i,X141] : (((X1 @ (kCOMB @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ (c_setsum @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty))) @ ((cCOMB @ ((sCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty))))) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))) @ (c_Inj1 @ c_Empty)))))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ (X140 @ (kCOMB @ (kCOMB @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ X138) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ X141) @ (c_Inj1 @ X141))))) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ (c_Inj1 @ (X140 @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ (c_Inj1 @ c_Empty)))) @ ((c_setsum @ c_Empty) @ c_Empty))))) => (! [X194 : $i > ($i > $i > $i) > $i > $i,X195,X196,X197 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((bCOMB @ c_setsum) @ ((cCOMB @ ((bCOMB @ X1) @ ((bCOMB @ kCOMB) @ kCOMB))) @ ((c_setsum @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))) @ c_Empty))) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ kCOMB))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X3 @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ X195) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (kCOMB @ ((X1 @ (kCOMB @ ((bCOMB @ X197) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)) @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))) @ c_Empty))) @ (c_Inj0 @ ((X3 @ (kCOMB @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty)))) @ (kCOMB @ ((X3 @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))) @ (kCOMB @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ ((c_setsum @ X195) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))) @ (((((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (kCOMB @ c_Empty)) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (kCOMB @ (kCOMB @ (c_Inj0 @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))))) @ X195))) @ ((c_setsum @ ((c_setsum @ X196) @ (((((X2 @ (kCOMB @ iCOMB)) @ (kCOMB @ (X197 @ (kCOMB @ (kCOMB @ c_Empty))))) @ (((X194 @ c_Empty) @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (((X194 @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))))) @ (kCOMB @ (X1 @ (kCOMB @ ((cCOMB @ ((cCOMB @ ((cCOMB @ iCOMB) @ (kCOMB @ (kCOMB @ c_Empty)))) @ c_Empty)) @ c_Empty))))) @ X195)))) => ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ X2)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ ((bCOMB @ (bCOMB @ kCOMB)) @ (cCOMB @ iCOMB)))))) @ iCOMB))) @ c_Empty))) @ ((cCOMB @ iCOMB) @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))) @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj0 @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((X1 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))))))))) @ (kCOMB @ (kCOMB @ ((bCOMB @ c_Inj1) @ ((bCOMB @ (X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))))) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((bCOMB @ kCOMB) @ ((cCOMB @ iCOMB) @ c_Empty))))))))))))) = ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ ((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ c_Empty)))))) @ (kCOMB @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) => (! [X336] : (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty))))) @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) = X336) => (c_False = $true)))))))))), 13.62/2.23 inference(fool_elimination,[],[f112])). 13.62/2.23 thf(f112,plain,( 13.62/2.23 ~! [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : (! [X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X7 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : (((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ ((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (((X1 @ (^[X13 : $i, X14 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))) @ (^[X15 : $i, X16 : $i, X17 : $i > $i] : (c_Empty)))) @ ((X1 @ (^[X18 : $i, X19 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ (((((X2 @ (^[X20 : $i, X21 : $i] : (((((X7 @ (^[X22 : $i > $i > $i] : (c_Empty))) @ (^[X23 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X24 : $i] : (c_Empty))) @ ((X6 @ (^[X25 : ($i > $i) > $i, X26 : $i > $i, X27 : $i] : (c_Empty))) @ c_Empty)) @ ((X1 @ (^[X28 : $i, X29 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty))))))) @ (^[X30 : $i] : (X30))) = (c_Inj1 @ c_Empty)) => (! [X32,X33 : $i > $i] : (((X3 @ (^[X35 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X36 : $i] : ((X33 @ X36)))) = (X33 @ ((c_setsum @ (((((X2 @ (^[X37 : $i, X38 : $i] : (((X1 @ (^[X39 : $i, X40 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (^[X41 : $i] : (X41))) @ X32) @ c_Empty) @ c_Empty)) @ ((X1 @ (^[X42 : $i, X43 : (($i > $i) > $i > $i) > $i > $i > $i] : ((((X43 @ (^[X44 : $i > $i, X45 : $i] : (c_Empty))) @ X42) @ (((((X2 @ (^[X46 : $i, X47 : $i] : (c_Empty))) @ (^[X48 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)))) => (! [X49,X52 : $i > $i] : ((((((X2 @ (^[X53 : $i, X54 : $i] : (c_Empty))) @ (^[X55 : $i] : ((((((X2 @ (^[X56 : $i, X57 : $i] : ((((((X2 @ (^[X58 : $i, X59 : $i] : (c_Empty))) @ (^[X60 : $i] : (c_Empty))) @ ((X0 @ (^[X61 : $i > $i, X62 : ($i > $i > $i) > $i > $i, X63 : $i, X64 : $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (^[X65 : $i, X66 : $i, X67 : $i > $i] : (((X0 @ (^[X68 : $i > $i, X69 : ($i > $i > $i) > $i > $i, X70 : $i, X71 : $i > $i] : (c_Empty))) @ (^[X72 : $i, X73 : $i, X74 : $i > $i] : (c_Empty))))))) @ (X52 @ X57)) @ X57)))) @ (^[X75 : $i] : (X55))) @ ((X1 @ (^[X76 : $i, X77 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ (((((X2 @ (^[X78 : $i, X79 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X80 : $i] : (((X1 @ (^[X81 : $i, X82 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))) @ ((X3 @ (^[X83 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X84 : $i] : (c_Empty)))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (^[X85 : $i > $i, X86 : ($i > $i > $i) > $i > $i, X87 : $i, X88 : $i > $i] : (c_Empty))) @ (^[X89 : $i, X90 : $i, X91 : $i > $i] : (c_Empty)))))) @ (X52 @ c_Empty)) @ c_Empty)))) @ X49) @ ((X0 @ (^[X92 : $i > $i, X93 : ($i > $i > $i) > $i > $i, X94 : $i, X95 : $i > $i] : ((c_Inj0 @ c_Empty)))) @ (^[X96 : $i, X97 : $i, X98 : $i > $i] : ((c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (^[X99 : $i, X100 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty))))))) @ ((c_setsum @ c_Empty) @ (X52 @ c_Empty))) = X49) => (! [X102 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X103 : (($i > $i > $i) > $i > $i) > $i,X104 : $i > $i] : ((((((X2 @ (^[X105 : $i, X106 : $i] : ((((((X2 @ (^[X107 : $i, X108 : $i] : (c_Empty))) @ (^[X109 : $i] : (X105))) @ (X104 @ c_Empty)) @ (X103 @ (^[X110 : $i > $i > $i, X111 : $i] : (((c_setsum @ c_Empty) @ ((X0 @ (^[X112 : $i > $i, X113 : ($i > $i > $i) > $i > $i, X114 : $i, X115 : $i > $i] : (c_Empty))) @ (^[X116 : $i, X117 : $i, X118 : $i > $i] : (c_Empty)))))))) @ c_Empty)))) @ (^[X119 : $i] : (c_Empty))) @ ((((X102 @ (^[X120 : ($i > $i) > $i, X121 : $i > $i, X122 : $i] : (c_Empty))) @ c_Empty) @ (((((X2 @ (^[X123 : $i, X124 : $i] : (((X3 @ (^[X125 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (X124))) @ (^[X126 : $i] : ((c_Inj0 @ c_Empty))))))) @ (^[X127 : $i] : (((X3 @ (^[X128 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((X103 @ (^[X129 : $i > $i > $i, X130 : $i] : (c_Empty)))))) @ (^[X131 : $i] : ((c_Inj0 @ c_Empty))))))) @ (X104 @ c_Empty)) @ c_Empty) @ ((((X102 @ (^[X132 : ($i > $i) > $i, X133 : $i > $i, X134 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X104 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X102 @ (^[X135 : ($i > $i) > $i, X136 : $i > $i, X137 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X104 @ (c_Inj1 @ c_Empty))) = (X104 @ (c_Inj0 @ c_Empty))) => (! [X138,X140 : (($i > $i) > $i > $i) > $i,X141] : (((X1 @ (^[X142 : $i, X143 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (^[X144 : $i, X145 : $i] : (c_Empty))) @ (^[X146 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (^[X147 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X148 : $i] : (c_Empty)))))) @ ((c_setsum @ ((c_setsum @ ((X0 @ (^[X149 : $i > $i, X150 : ($i > $i > $i) > $i > $i, X151 : $i, X152 : $i > $i] : (c_Empty))) @ (^[X153 : $i, X154 : $i, X155 : $i > $i] : (c_Empty)))) @ c_Empty)) @ (((X143 @ (^[X156 : $i > $i, X157 : $i] : ((c_Inj0 @ c_Empty)))) @ (((X143 @ (^[X158 : $i > $i, X159 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)) @ (c_Inj1 @ c_Empty))))))) @ (((((X2 @ (^[X160 : $i, X161 : $i] : (c_Empty))) @ (^[X162 : $i] : ((X140 @ (^[X163 : $i > $i, X164 : $i] : (((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (^[X165 : $i, X166 : $i] : (c_Empty))) @ (^[X167 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ X138) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (^[X168 : $i, X169 : $i] : (((c_setsum @ X141) @ (c_Inj1 @ X141))))) @ (^[X170 : $i] : (((X0 @ (^[X171 : $i > $i, X172 : ($i > $i > $i) > $i > $i, X173 : $i, X174 : $i > $i] : ((c_Inj1 @ c_Empty)))) @ (^[X175 : $i, X176 : $i, X177 : $i > $i] : (c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (^[X178 : $i > $i, X179 : ($i > $i > $i) > $i > $i, X180 : $i, X181 : $i > $i] : ((c_Inj1 @ c_Empty)))) @ (^[X182 : $i, X183 : $i, X184 : $i > $i] : ((c_Inj0 @ (((((X2 @ (^[X185 : $i, X186 : $i] : (c_Empty))) @ (^[X187 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ (c_Inj1 @ (X140 @ (^[X188 : $i > $i, X189 : $i] : ((c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ (^[X190 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((((X190 @ (^[X191 : $i > $i > $i, X192 : $i > $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X193 : $i] : ((c_Inj1 @ c_Empty))))) @ ((c_setsum @ c_Empty) @ c_Empty))))) => (! [X194 : $i > ($i > $i > $i) > $i > $i,X195,X196,X197 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ (^[X198 : $i, X199 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ ((X1 @ (^[X200 : $i, X201 : (($i > $i) > $i > $i) > $i > $i > $i] : (X198))) @ ((c_setsum @ (((((X2 @ (^[X202 : $i, X203 : $i] : (c_Empty))) @ (^[X204 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (^[X205 : $i, X206 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))) @ c_Empty)))) @ (((((X2 @ (^[X207 : $i, X208 : $i] : (X208))) @ (^[X209 : $i] : (((X0 @ (^[X210 : $i > $i, X211 : ($i > $i > $i) > $i > $i, X212 : $i, X213 : $i > $i] : (X212))) @ (^[X214 : $i, X215 : $i, X216 : $i > $i] : (((X3 @ (^[X217 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((((X217 @ (^[X218 : $i > $i > $i, X219 : $i > $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X220 : $i] : (c_Empty))))))))) @ X195) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (^[X221 : $i, X222 : $i] : (c_Empty))) @ (^[X223 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (^[X224 : $i, X225 : $i] : ((c_Inj0 @ c_Empty)))) @ (^[X226 : $i] : (((X1 @ (^[X227 : $i, X228 : (($i > $i) > $i > $i) > $i > $i > $i] : ((X197 @ (^[X229 : $i > $i > $i, X230 : $i] : ((((X228 @ (^[X231 : $i > $i, X232 : $i] : ((((((X2 @ (^[X233 : $i, X234 : $i] : (c_Empty))) @ (^[X235 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))) @ c_Empty) @ ((X1 @ (^[X236 : $i, X237 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))))))) @ c_Empty)))) @ (c_Inj0 @ ((X3 @ (^[X238 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (^[X239 : $i] : (((X3 @ (^[X240 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (^[X241 : $i] : ((((((X2 @ (^[X242 : $i, X243 : $i] : (c_Empty))) @ (^[X244 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))))))) @ ((c_setsum @ ((c_setsum @ X195) @ ((X1 @ (^[X245 : $i, X246 : (($i > $i) > $i > $i) > $i > $i > $i] : ((c_Inj0 @ c_Empty)))) @ (((((X2 @ (^[X247 : $i, X248 : $i] : (c_Empty))) @ (^[X249 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (^[X250 : $i, X251 : (($i > $i) > $i > $i) > $i > $i > $i] : ((c_Inj0 @ ((X0 @ (^[X252 : $i > $i, X253 : ($i > $i > $i) > $i > $i, X254 : $i, X255 : $i > $i] : (c_Empty))) @ (^[X256 : $i, X257 : $i, X258 : $i > $i] : (c_Empty))))))) @ X195))) @ ((c_setsum @ ((c_setsum @ X196) @ (((((X2 @ (^[X259 : $i, X260 : $i] : (X260))) @ (^[X261 : $i] : ((X197 @ (^[X262 : $i > $i > $i, X263 : $i] : (c_Empty)))))) @ (((X194 @ c_Empty) @ (^[X264 : $i, X265 : $i] : (c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (^[X266 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X267 : $i] : (c_Empty)))))) @ (((X194 @ ((X3 @ (^[X268 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X269 : $i] : (((X0 @ (^[X270 : $i > $i, X271 : ($i > $i > $i) > $i > $i, X272 : $i, X273 : $i > $i] : (c_Empty))) @ (^[X274 : $i, X275 : $i, X276 : $i > $i] : (c_Empty))))))) @ (^[X277 : $i, X278 : $i] : (((X1 @ (^[X279 : $i, X280 : (($i > $i) > $i > $i) > $i > $i > $i] : ((((X280 @ (^[X281 : $i > $i, X282 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ X278)))) @ X195)))) => ((((X0 @ (^[X287 : $i > $i, X288 : ($i > $i > $i) > $i > $i, X289 : $i, X290 : $i > $i] : (c_Empty))) @ (^[X291 : $i, X292 : $i, X293 : $i > $i] : (((X0 @ (^[X294 : $i > $i, X295 : ($i > $i > $i) > $i > $i, X296 : $i, X297 : $i > $i] : ((((((X2 @ (^[X298 : $i, X299 : $i] : ((X297 @ X296)))) @ (^[X300 : $i] : (X300))) @ c_Empty) @ (X297 @ ((X3 @ (^[X301 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X302 : $i] : (c_Empty))))) @ ((X0 @ (^[X303 : $i > $i, X304 : ($i > $i > $i) > $i > $i, X305 : $i, X306 : $i > $i] : ((c_Inj0 @ c_Empty)))) @ (^[X307 : $i, X308 : $i, X309 : $i > $i] : (((X1 @ (^[X310 : $i, X311 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))))))) @ (^[X312 : $i, X313 : $i, X314 : $i > $i] : ((c_Inj1 @ ((X0 @ (^[X315 : $i > $i, X316 : ($i > $i > $i) > $i > $i, X317 : $i, X318 : $i > $i] : (c_Empty))) @ (^[X319 : $i, X320 : $i, X321 : $i > $i] : ((X314 @ c_Empty))))))))))) = ((X0 @ (^[X322 : $i > $i, X323 : ($i > $i > $i) > $i > $i, X324 : $i, X325 : $i > $i] : (((c_setsum @ ((X0 @ (^[X326 : $i > $i, X327 : ($i > $i > $i) > $i > $i, X328 : $i, X329 : $i > $i] : (c_Empty))) @ (^[X330 : $i, X331 : $i, X332 : $i > $i] : (c_Empty)))) @ c_Empty)))) @ (^[X333 : $i, X334 : $i, X335 : $i > $i] : (((c_setsum @ c_Empty) @ c_Empty))))) => (! [X336] : (((X0 @ (^[X340 : $i > $i, X341 : ($i > $i > $i) > $i > $i, X342 : $i, X343 : $i > $i] : (c_Empty))) @ (^[X344 : $i, X345 : $i, X346 : $i > $i] : (c_Empty))) = X336) => c_False))))))))), 13.62/2.23 inference(rectify,[],[f5])). 13.62/2.23 thf(f5,negated_conjecture,( 13.62/2.23 ~! [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : (! [X4 : ($i > $i > $i) > $i,X5,X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X7 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : (((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ ((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (((X1 @ (^[X13 : $i, X14 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty)))) @ ((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ (((((X2 @ (^[X9 : $i, X10 : $i] : (((((X7 @ (^[X11 : $i > $i > $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X9 : $i] : (c_Empty))) @ ((X6 @ (^[X9 : ($i > $i) > $i, X10 : $i > $i, X11 : $i] : (c_Empty))) @ c_Empty)) @ ((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty))))))) @ (^[X8 : $i] : (X8))) = (c_Inj1 @ c_Empty)) => (! [X4,X5,X6 : $i > $i,X7] : (((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X8 : $i] : ((X6 @ X8)))) = (X6 @ ((c_setsum @ (((((X2 @ (^[X8 : $i, X9 : $i] : (((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (^[X8 : $i] : (X8))) @ X5) @ c_Empty) @ c_Empty)) @ ((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : ((((X9 @ (^[X10 : $i > $i, X11 : $i] : (c_Empty))) @ X8) @ (((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)))) => (! [X4,X5 : ($i > ($i > $i) > $i) > $i,X6,X7 : $i > $i] : ((((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : ((((((X2 @ (^[X9 : $i, X10 : $i] : ((((((X2 @ (^[X11 : $i, X12 : $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ ((X0 @ (^[X11 : $i > $i, X12 : ($i > $i > $i) > $i > $i, X13 : $i, X14 : $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (^[X11 : $i, X12 : $i, X13 : $i > $i] : (((X0 @ (^[X14 : $i > $i, X15 : ($i > $i > $i) > $i > $i, X16 : $i, X17 : $i > $i] : (c_Empty))) @ (^[X14 : $i, X15 : $i, X16 : $i > $i] : (c_Empty))))))) @ (X7 @ X10)) @ X10)))) @ (^[X9 : $i] : (X8))) @ ((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ (((((X2 @ (^[X9 : $i, X10 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X9 : $i] : (((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))) @ ((X3 @ (^[X9 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X9 : $i] : (c_Empty)))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (c_Empty))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty)))))) @ (X7 @ c_Empty)) @ c_Empty)))) @ X4) @ ((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : ((c_Inj0 @ c_Empty)))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : ((c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (^[X11 : $i, X12 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty))))))) @ ((c_setsum @ c_Empty) @ (X7 @ c_Empty))) = X4) => (! [X4 : $i > $i > $i,X5 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X6 : (($i > $i > $i) > $i > $i) > $i,X7 : $i > $i] : ((((((X2 @ (^[X8 : $i, X9 : $i] : ((((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (X8))) @ (X7 @ c_Empty)) @ (X6 @ (^[X10 : $i > $i > $i, X11 : $i] : (((c_setsum @ c_Empty) @ ((X0 @ (^[X12 : $i > $i, X13 : ($i > $i > $i) > $i > $i, X14 : $i, X15 : $i > $i] : (c_Empty))) @ (^[X12 : $i, X13 : $i, X14 : $i > $i] : (c_Empty)))))))) @ c_Empty)))) @ (^[X8 : $i] : (c_Empty))) @ ((((X5 @ (^[X8 : ($i > $i) > $i, X9 : $i > $i, X10 : $i] : (c_Empty))) @ c_Empty) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (((X3 @ (^[X10 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (X9))) @ (^[X10 : $i] : ((c_Inj0 @ c_Empty))))))) @ (^[X8 : $i] : (((X3 @ (^[X9 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((X6 @ (^[X10 : $i > $i > $i, X11 : $i] : (c_Empty)))))) @ (^[X9 : $i] : ((c_Inj0 @ c_Empty))))))) @ (X7 @ c_Empty)) @ c_Empty) @ ((((X5 @ (^[X8 : ($i > $i) > $i, X9 : $i > $i, X10 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X7 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X5 @ (^[X8 : ($i > $i) > $i, X9 : $i > $i, X10 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X7 @ (c_Inj1 @ c_Empty))) = (X7 @ (c_Inj0 @ c_Empty))) => (! [X4,X5 : $i > $i > ($i > $i) > $i > $i,X6 : (($i > $i) > $i > $i) > $i,X7] : (((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (^[X10 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty)))))) @ ((c_setsum @ ((c_setsum @ ((X0 @ (^[X10 : $i > $i, X11 : ($i > $i > $i) > $i > $i, X12 : $i, X13 : $i > $i] : (c_Empty))) @ (^[X10 : $i, X11 : $i, X12 : $i > $i] : (c_Empty)))) @ c_Empty)) @ (((X9 @ (^[X10 : $i > $i, X11 : $i] : ((c_Inj0 @ c_Empty)))) @ (((X9 @ (^[X10 : $i > $i, X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)) @ (c_Inj1 @ c_Empty))))))) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : ((X6 @ (^[X9 : $i > $i, X10 : $i] : (((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (^[X11 : $i, X12 : $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ X4) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (^[X8 : $i, X9 : $i] : (((c_setsum @ X7) @ (c_Inj1 @ X7))))) @ (^[X8 : $i] : (((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : ((c_Inj1 @ c_Empty)))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : ((c_Inj1 @ c_Empty)))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : ((c_Inj0 @ (((((X2 @ (^[X11 : $i, X12 : $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ (c_Inj1 @ (X6 @ (^[X8 : $i > $i, X9 : $i] : ((c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((((X8 @ (^[X9 : $i > $i > $i, X10 : $i > $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X8 : $i] : ((c_Inj1 @ c_Empty))))) @ ((c_setsum @ c_Empty) @ c_Empty))))) => (! [X4 : $i > ($i > $i > $i) > $i > $i,X5,X6,X7 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ ((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (X8))) @ ((c_setsum @ (((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))) @ c_Empty)))) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (X9))) @ (^[X8 : $i] : (((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (X11))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (((X3 @ (^[X12 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((((X12 @ (^[X13 : $i > $i > $i, X14 : $i > $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X12 : $i] : (c_Empty))))))))) @ X5) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (^[X8 : $i, X9 : $i] : ((c_Inj0 @ c_Empty)))) @ (^[X8 : $i] : (((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : ((X7 @ (^[X11 : $i > $i > $i, X12 : $i] : ((((X10 @ (^[X13 : $i > $i, X14 : $i] : ((((((X2 @ (^[X15 : $i, X16 : $i] : (c_Empty))) @ (^[X15 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))) @ c_Empty) @ ((X1 @ (^[X13 : $i, X14 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))))))) @ c_Empty)))) @ (c_Inj0 @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (^[X8 : $i] : (((X3 @ (^[X9 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (^[X9 : $i] : ((((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))))))) @ ((c_setsum @ ((c_setsum @ X5) @ ((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : ((c_Inj0 @ c_Empty)))) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : ((c_Inj0 @ ((X0 @ (^[X10 : $i > $i, X11 : ($i > $i > $i) > $i > $i, X12 : $i, X13 : $i > $i] : (c_Empty))) @ (^[X10 : $i, X11 : $i, X12 : $i > $i] : (c_Empty))))))) @ X5))) @ ((c_setsum @ ((c_setsum @ X6) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (X9))) @ (^[X8 : $i] : ((X7 @ (^[X9 : $i > $i > $i, X10 : $i] : (c_Empty)))))) @ (((X4 @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X8 : $i] : (c_Empty)))))) @ (((X4 @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X8 : $i] : (((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (c_Empty))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty))))))) @ (^[X8 : $i, X9 : $i] : (((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : ((((X11 @ (^[X12 : $i > $i, X13 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ X9)))) @ X5)))) => (! [X4 : ($i > $i) > $i,X5 : $i > $i,X6,X7] : (((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : (c_Empty))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : (((X0 @ (^[X11 : $i > $i, X12 : ($i > $i > $i) > $i > $i, X13 : $i, X14 : $i > $i] : ((((((X2 @ (^[X15 : $i, X16 : $i] : ((X14 @ X13)))) @ (^[X15 : $i] : (X15))) @ c_Empty) @ (X14 @ ((X3 @ (^[X15 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X15 : $i] : (c_Empty))))) @ ((X0 @ (^[X15 : $i > $i, X16 : ($i > $i > $i) > $i > $i, X17 : $i, X18 : $i > $i] : ((c_Inj0 @ c_Empty)))) @ (^[X15 : $i, X16 : $i, X17 : $i > $i] : (((X1 @ (^[X18 : $i, X19 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))))))) @ (^[X11 : $i, X12 : $i, X13 : $i > $i] : ((c_Inj1 @ ((X0 @ (^[X14 : $i > $i, X15 : ($i > $i > $i) > $i > $i, X16 : $i, X17 : $i > $i] : (c_Empty))) @ (^[X14 : $i, X15 : $i, X16 : $i > $i] : ((X13 @ c_Empty))))))))))) = ((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : (((c_setsum @ ((X0 @ (^[X12 : $i > $i, X13 : ($i > $i > $i) > $i > $i, X14 : $i, X15 : $i > $i] : (c_Empty))) @ (^[X12 : $i, X13 : $i, X14 : $i > $i] : (c_Empty)))) @ c_Empty)))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : (((c_setsum @ c_Empty) @ c_Empty))))) => (! [X4,X5,X6,X7] : (((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : (c_Empty))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : (c_Empty))) = X4) => c_False))))))))), 13.62/2.23 inference(negated_conjecture,[],[f4])). 13.62/2.23 thf(f4,conjecture,( 13.62/2.23 ! [X0 : (($i > $i) > (($i > $i > $i) > $i > $i) > $i > ($i > $i) > $i) > ($i > $i > ($i > $i) > $i) > $i,X1 : ($i > ((($i > $i) > $i > $i) > $i > $i > $i) > $i) > $i > $i,X2 : ($i > $i > $i) > ($i > $i) > $i > $i > $i > $i,X3 : (((($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i) > $i) > ($i > $i) > $i] : (! [X4 : ($i > $i > $i) > $i,X5,X6 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i,X7 : (($i > $i > $i) > $i) > ($i > $i) > $i > $i > $i] : (((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ ((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (((X1 @ (^[X13 : $i, X14 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty))))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty)))) @ ((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ (((((X2 @ (^[X9 : $i, X10 : $i] : (((((X7 @ (^[X11 : $i > $i > $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X9 : $i] : (c_Empty))) @ ((X6 @ (^[X9 : ($i > $i) > $i, X10 : $i > $i, X11 : $i] : (c_Empty))) @ c_Empty)) @ ((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty))))))) @ (^[X8 : $i] : (X8))) = (c_Inj1 @ c_Empty)) => (! [X4,X5,X6 : $i > $i,X7] : (((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X8 : $i] : ((X6 @ X8)))) = (X6 @ ((c_setsum @ (((((X2 @ (^[X8 : $i, X9 : $i] : (((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (^[X8 : $i] : (X8))) @ X5) @ c_Empty) @ c_Empty)) @ ((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : ((((X9 @ (^[X10 : $i > $i, X11 : $i] : (c_Empty))) @ X8) @ (((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))) @ c_Empty)))) => (! [X4,X5 : ($i > ($i > $i) > $i) > $i,X6,X7 : $i > $i] : ((((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : ((((((X2 @ (^[X9 : $i, X10 : $i] : ((((((X2 @ (^[X11 : $i, X12 : $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ ((X0 @ (^[X11 : $i > $i, X12 : ($i > $i > $i) > $i > $i, X13 : $i, X14 : $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (^[X11 : $i, X12 : $i, X13 : $i > $i] : (((X0 @ (^[X14 : $i > $i, X15 : ($i > $i > $i) > $i > $i, X16 : $i, X17 : $i > $i] : (c_Empty))) @ (^[X14 : $i, X15 : $i, X16 : $i > $i] : (c_Empty))))))) @ (X7 @ X10)) @ X10)))) @ (^[X9 : $i] : (X8))) @ ((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ (((((X2 @ (^[X9 : $i, X10 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X9 : $i] : (((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))) @ ((X3 @ (^[X9 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X9 : $i] : (c_Empty)))) @ (c_Inj1 @ c_Empty)) @ ((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (c_Empty))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty)))))) @ (X7 @ c_Empty)) @ c_Empty)))) @ X4) @ ((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : ((c_Inj0 @ c_Empty)))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : ((c_Inj0 @ ((c_setsum @ (c_Inj0 @ c_Empty)) @ ((X1 @ (^[X11 : $i, X12 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty))))))) @ ((c_setsum @ c_Empty) @ (X7 @ c_Empty))) = X4) => (! [X4 : $i > $i > $i,X5 : ((($i > $i) > $i) > ($i > $i) > $i > $i) > $i > $i > $i > $i,X6 : (($i > $i > $i) > $i > $i) > $i,X7 : $i > $i] : ((((((X2 @ (^[X8 : $i, X9 : $i] : ((((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (X8))) @ (X7 @ c_Empty)) @ (X6 @ (^[X10 : $i > $i > $i, X11 : $i] : (((c_setsum @ c_Empty) @ ((X0 @ (^[X12 : $i > $i, X13 : ($i > $i > $i) > $i > $i, X14 : $i, X15 : $i > $i] : (c_Empty))) @ (^[X12 : $i, X13 : $i, X14 : $i > $i] : (c_Empty)))))))) @ c_Empty)))) @ (^[X8 : $i] : (c_Empty))) @ ((((X5 @ (^[X8 : ($i > $i) > $i, X9 : $i > $i, X10 : $i] : (c_Empty))) @ c_Empty) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (((X3 @ (^[X10 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (X9))) @ (^[X10 : $i] : ((c_Inj0 @ c_Empty))))))) @ (^[X8 : $i] : (((X3 @ (^[X9 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((X6 @ (^[X10 : $i > $i > $i, X11 : $i] : (c_Empty)))))) @ (^[X9 : $i] : ((c_Inj0 @ c_Empty))))))) @ (X7 @ c_Empty)) @ c_Empty) @ ((((X5 @ (^[X8 : ($i > $i) > $i, X9 : $i > $i, X10 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (c_Inj1 @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ c_Empty))) @ (c_Inj0 @ ((c_setsum @ (c_Inj1 @ c_Empty)) @ (X7 @ c_Empty))))) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ ((((X5 @ (^[X8 : ($i > $i) > $i, X9 : $i > $i, X10 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (X7 @ (c_Inj1 @ c_Empty))) = (X7 @ (c_Inj0 @ c_Empty))) => (! [X4,X5 : $i > $i > ($i > $i) > $i > $i,X6 : (($i > $i) > $i > $i) > $i,X7] : (((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ ((c_setsum @ ((c_setsum @ c_Empty) @ c_Empty)) @ ((c_setsum @ (((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X3 @ (^[X10 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty)))))) @ ((c_setsum @ ((c_setsum @ ((X0 @ (^[X10 : $i > $i, X11 : ($i > $i > $i) > $i > $i, X12 : $i, X13 : $i > $i] : (c_Empty))) @ (^[X10 : $i, X11 : $i, X12 : $i > $i] : (c_Empty)))) @ c_Empty)) @ (((X9 @ (^[X10 : $i > $i, X11 : $i] : ((c_Inj0 @ c_Empty)))) @ (((X9 @ (^[X10 : $i > $i, X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)) @ (c_Inj1 @ c_Empty))))))) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : ((X6 @ (^[X9 : $i > $i, X10 : $i] : (((c_setsum @ (c_Inj1 @ c_Empty)) @ (((((X2 @ (^[X11 : $i, X12 : $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))))))) @ ((c_setsum @ X4) @ (c_Inj1 @ ((c_setsum @ c_Empty) @ c_Empty)))) @ c_Empty) @ (c_Inj0 @ c_Empty))) = (((((X2 @ (^[X8 : $i, X9 : $i] : (((c_setsum @ X7) @ (c_Inj1 @ X7))))) @ (^[X8 : $i] : (((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : ((c_Inj1 @ c_Empty)))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty)))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ ((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : ((c_Inj1 @ c_Empty)))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : ((c_Inj0 @ (((((X2 @ (^[X11 : $i, X12 : $i] : (c_Empty))) @ (^[X11 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))))) @ ((c_setsum @ (c_Inj1 @ (X6 @ (^[X8 : $i > $i, X9 : $i] : ((c_Inj1 @ c_Empty)))))) @ ((c_setsum @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((((X8 @ (^[X9 : $i > $i > $i, X10 : $i > $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X8 : $i] : ((c_Inj1 @ c_Empty))))) @ ((c_setsum @ c_Empty) @ c_Empty))))) => (! [X4 : $i > ($i > $i > $i) > $i > $i,X5,X6,X7 : (($i > $i > $i) > $i > $i) > $i] : (((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : (((c_setsum @ ((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (X8))) @ ((c_setsum @ (((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)) @ ((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))) @ c_Empty)))) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (X9))) @ (^[X8 : $i] : (((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (X11))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (((X3 @ (^[X12 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : ((((X12 @ (^[X13 : $i > $i > $i, X14 : $i > $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ (^[X12 : $i] : (c_Empty))))))))) @ X5) @ (c_Inj1 @ (c_Inj0 @ c_Empty))) @ ((c_setsum @ c_Empty) @ (c_Inj1 @ (((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))) = (((((X2 @ (^[X8 : $i, X9 : $i] : ((c_Inj0 @ c_Empty)))) @ (^[X8 : $i] : (((X1 @ (^[X9 : $i, X10 : (($i > $i) > $i > $i) > $i > $i > $i] : ((X7 @ (^[X11 : $i > $i > $i, X12 : $i] : ((((X10 @ (^[X13 : $i > $i, X14 : $i] : ((((((X2 @ (^[X15 : $i, X16 : $i] : (c_Empty))) @ (^[X15 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))) @ c_Empty) @ ((X1 @ (^[X13 : $i, X14 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))))))) @ c_Empty)))) @ (c_Inj0 @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ (c_Inj0 @ c_Empty)) @ ((c_setsum @ c_Empty) @ c_Empty))))) @ (^[X8 : $i] : (((X3 @ (^[X9 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ (^[X9 : $i] : ((((((X2 @ (^[X10 : $i, X11 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty))))))))) @ ((c_setsum @ ((c_setsum @ X5) @ ((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : ((c_Inj0 @ c_Empty)))) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ (^[X8 : $i] : (c_Empty))) @ c_Empty) @ c_Empty) @ c_Empty)))) @ ((X1 @ (^[X8 : $i, X9 : (($i > $i) > $i > $i) > $i > $i > $i] : ((c_Inj0 @ ((X0 @ (^[X10 : $i > $i, X11 : ($i > $i > $i) > $i > $i, X12 : $i, X13 : $i > $i] : (c_Empty))) @ (^[X10 : $i, X11 : $i, X12 : $i > $i] : (c_Empty))))))) @ X5))) @ ((c_setsum @ ((c_setsum @ X6) @ (((((X2 @ (^[X8 : $i, X9 : $i] : (X9))) @ (^[X8 : $i] : ((X7 @ (^[X9 : $i > $i > $i, X10 : $i] : (c_Empty)))))) @ (((X4 @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty))) @ c_Empty)) @ (c_Inj0 @ c_Empty)) @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X8 : $i] : (c_Empty)))))) @ (((X4 @ ((X3 @ (^[X8 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X8 : $i] : (((X0 @ (^[X9 : $i > $i, X10 : ($i > $i > $i) > $i > $i, X11 : $i, X12 : $i > $i] : (c_Empty))) @ (^[X9 : $i, X10 : $i, X11 : $i > $i] : (c_Empty))))))) @ (^[X8 : $i, X9 : $i] : (((X1 @ (^[X10 : $i, X11 : (($i > $i) > $i > $i) > $i > $i > $i] : ((((X11 @ (^[X12 : $i > $i, X13 : $i] : (c_Empty))) @ c_Empty) @ c_Empty)))) @ X9)))) @ X5)))) => (! [X4 : ($i > $i) > $i,X5 : $i > $i,X6,X7] : (((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : (c_Empty))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : (((X0 @ (^[X11 : $i > $i, X12 : ($i > $i > $i) > $i > $i, X13 : $i, X14 : $i > $i] : ((((((X2 @ (^[X15 : $i, X16 : $i] : ((X14 @ X13)))) @ (^[X15 : $i] : (X15))) @ c_Empty) @ (X14 @ ((X3 @ (^[X15 : (($i > $i > $i) > ($i > $i) > $i) > $i > $i > $i] : (c_Empty))) @ (^[X15 : $i] : (c_Empty))))) @ ((X0 @ (^[X15 : $i > $i, X16 : ($i > $i > $i) > $i > $i, X17 : $i, X18 : $i > $i] : ((c_Inj0 @ c_Empty)))) @ (^[X15 : $i, X16 : $i, X17 : $i > $i] : (((X1 @ (^[X18 : $i, X19 : (($i > $i) > $i > $i) > $i > $i > $i] : (c_Empty))) @ c_Empty)))))))) @ (^[X11 : $i, X12 : $i, X13 : $i > $i] : ((c_Inj1 @ ((X0 @ (^[X14 : $i > $i, X15 : ($i > $i > $i) > $i > $i, X16 : $i, X17 : $i > $i] : (c_Empty))) @ (^[X14 : $i, X15 : $i, X16 : $i > $i] : ((X13 @ c_Empty))))))))))) = ((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : (((c_setsum @ ((X0 @ (^[X12 : $i > $i, X13 : ($i > $i > $i) > $i > $i, X14 : $i, X15 : $i > $i] : (c_Empty))) @ (^[X12 : $i, X13 : $i, X14 : $i > $i] : (c_Empty)))) @ c_Empty)))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : (((c_setsum @ c_Empty) @ c_Empty))))) => (! [X4,X5,X6,X7] : (((X0 @ (^[X8 : $i > $i, X9 : ($i > $i > $i) > $i > $i, X10 : $i, X11 : $i > $i] : (c_Empty))) @ (^[X8 : $i, X9 : $i, X10 : $i > $i] : (c_Empty))) = X4) => c_False))))))))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)). 13.62/2.23 thf(f405,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ ((c_Repl @ X0) @ X1))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))))) @ (vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))) @ ((c_In @ X2) @ ((c_Repl @ X0) @ X1))))))) @ iCOMB)))) )), 13.62/2.23 inference(combinator_demodulation,[],[f398])). 13.62/2.23 thf(f398,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (($true = ((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))) @ vIMP))) @ (cCOMB @ vIMP)) @ ((c_In @ X2) @ ((c_Repl @ X0) @ X1))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))))) )), 13.62/2.23 inference(definition_unfolding,[],[f323,f385,f369])). 13.62/2.23 thf(f369,plain,( 13.62/2.23 (c_and = ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))), 13.62/2.23 inference(cnf_transformation,[],[f263])). 13.62/2.23 thf(f263,plain,( 13.62/2.23 (c_and = ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))), 13.62/2.23 inference(fool_elimination,[],[f262])). 13.62/2.23 thf(f262,plain,( 13.62/2.23 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))), 13.62/2.23 inference(rectify,[],[f99])). 13.62/2.23 thf(f99,axiom,( 13.62/2.23 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14)). 13.62/2.23 thf(f385,plain,( 13.62/2.23 (c_iff = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))) @ vIMP))) @ (cCOMB @ vIMP)))), 13.62/2.23 inference(definition_unfolding,[],[f374,f369])). 13.62/2.23 thf(f374,plain,( 13.62/2.23 (c_iff = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ c_and)) @ vIMP))) @ (cCOMB @ vIMP)))), 13.62/2.23 inference(cnf_transformation,[],[f226])). 13.62/2.23 thf(f226,plain,( 13.62/2.23 (c_iff = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ c_and)) @ vIMP))) @ (cCOMB @ vIMP)))), 13.62/2.23 inference(fool_elimination,[],[f225])). 13.62/2.23 thf(f225,plain,( 13.62/2.23 (c_iff = (^[X0 : $o, X1 : $o] : (((c_and @ X0 => X1) @ X1 => X0))))), 13.62/2.23 inference(rectify,[],[f32])). 13.62/2.23 thf(f32,axiom,( 13.62/2.23 (c_iff = (^[X0 : $o, X1 : $o] : (((c_and @ X0 => X1) @ X1 => X0))))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16)). 13.62/2.23 thf(f323,plain,( 13.62/2.23 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (($true = ((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ X1))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ c_and) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))))) )), 13.62/2.23 inference(cnf_transformation,[],[f285])). 13.62/2.23 thf(f285,plain,( 13.62/2.23 ! [X0,X1 : $i > $i,X2] : ($true = ((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ X1))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ c_and) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ X1)) @ X2)))))), 13.62/2.23 inference(fool_elimination,[],[f284])). 13.62/2.23 thf(f284,plain,( 13.62/2.23 ! [X0,X1 : $i > $i,X2] : ((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ (^[X3 : $i] : ((X1 @ X3)))))) @ ? [X4] : ((c_and @ ((c_In @ X4) @ X0)) @ ((X1 @ X4) = X2)))), 13.62/2.23 inference(rectify,[],[f26])). 13.62/2.23 thf(f26,axiom,( 13.62/2.23 ! [X0,X1 : $i > $i,X2] : ((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ (^[X3 : $i] : ((X1 @ X3)))))) @ ? [X3] : ((c_and @ ((c_In @ X3) @ X0)) @ ((X1 @ X3) = X2)))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8)). 13.62/2.23 thf(f407,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X1) @ (c_Power @ X0))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X1))) @ ((cCOMB @ c_In) @ X0)))))) @ (vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X1))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X1) @ (c_Power @ X0))))))) @ iCOMB)))) )), 13.62/2.23 inference(combinator_demodulation,[],[f400])). 13.62/2.23 thf(f400,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($true = ((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))) @ vIMP))) @ (cCOMB @ vIMP)) @ ((c_In @ X1) @ (c_Power @ X0))) @ ((((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ c_In))))) @ (cCOMB @ c_In))) @ X1) @ X0)))) )), 13.62/2.23 inference(definition_unfolding,[],[f325,f385,f378])). 13.62/2.23 thf(f378,plain,( 13.62/2.23 (c_Subq = ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ c_In))))) @ (cCOMB @ c_In))))), 13.62/2.23 inference(cnf_transformation,[],[f239])). 13.62/2.23 thf(f239,plain,( 13.62/2.23 (c_Subq = ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ c_In))))) @ (cCOMB @ c_In))))), 13.62/2.23 inference(fool_elimination,[],[f238])). 13.62/2.23 thf(f238,plain,( 13.62/2.23 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2] : (((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))), 13.62/2.23 inference(rectify,[],[f92])). 13.62/2.23 thf(f92,axiom,( 13.62/2.23 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2] : (((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17)). 13.62/2.23 thf(f325,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : ((((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0)) = $true)) )), 13.62/2.23 inference(cnf_transformation,[],[f281])). 13.62/2.23 thf(f281,plain,( 13.62/2.23 ! [X0,X1] : (((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0)) = $true)), 13.62/2.23 inference(fool_elimination,[],[f280])). 13.62/2.23 thf(f280,plain,( 13.62/2.23 ! [X0,X1] : ((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))), 13.62/2.23 inference(rectify,[],[f44])). 13.62/2.23 thf(f44,axiom,( 13.62/2.23 ! [X0,X1] : ((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7)). 13.62/2.23 thf(f1854,plain,( 13.62/2.23 spl11_1 | spl11_2), 13.62/2.23 inference(avatar_split_clause,[],[f1598,f1845,f1842])). 13.62/2.23 thf(f1598,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((c_In @ X1) @ X0) = $false) | ($true = X2)) )), 13.62/2.23 inference(combinator_demodulation,[],[f1597])). 13.62/2.23 thf(f1597,plain,( 13.62/2.23 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((c_In @ X1) @ X0) = $false) | ($true = (iCOMB @ X2))) )), 13.62/2.23 inference(pi_clausification,[],[f1596])). 13.62/2.23 thf(f1596,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : ((((c_In @ X1) @ X0) = $false) | ($true = (vPI($o) @ iCOMB))) )), 13.62/2.23 inference(combinator_demodulation,[],[f1595])). 13.62/2.23 thf(f1595,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : (($false = (((cCOMB @ c_In) @ X0) @ X1)) | ($true = (vPI($o) @ iCOMB))) )), 13.62/2.23 inference(pi_clausification,[],[f1594])). 13.62/2.23 thf(f1594,plain,( 13.62/2.23 ( ! [X0 : $i] : (($false = (vSIGMA($i) @ ((cCOMB @ c_In) @ X0))) | ($true = (vPI($o) @ iCOMB))) )), 13.62/2.23 inference(binary_proxy_clausification,[],[f1104])). 13.62/2.23 thf(f1104,plain,( 13.62/2.23 ( ! [X0 : $i] : (($true = ((vIMP @ (vSIGMA($i) @ ((cCOMB @ c_In) @ X0))) @ (vPI($o) @ iCOMB)))) )), 13.62/2.23 inference(superposition,[],[f404,f466])). 13.62/2.23 thf(f466,plain,( 13.62/2.23 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )), 13.62/2.23 inference(superposition,[],[f320,f320])). 13.62/2.23 thf(f404,plain,( 13.62/2.23 ($true = ((vIMP @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))) @ (vPI($o) @ iCOMB)))), 13.62/2.23 inference(combinator_demodulation,[],[f397])). 13.62/2.23 thf(f397,plain,( 13.62/2.23 ($true = (((cCOMB @ vIMP) @ (vPI($o) @ iCOMB)) @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))))), 13.62/2.23 inference(definition_unfolding,[],[f322,f386])). 13.62/2.23 thf(f386,plain,( 13.62/2.23 (c_not = ((cCOMB @ vIMP) @ (vPI($o) @ iCOMB)))), 13.62/2.23 inference(definition_unfolding,[],[f367,f368])). 13.62/2.23 thf(f368,plain,( 13.62/2.23 (c_False = (vPI($o) @ iCOMB))), 13.62/2.23 inference(cnf_transformation,[],[f204])). 13.62/2.23 thf(f204,plain,( 13.62/2.23 (c_False = (vPI($o) @ iCOMB))), 13.62/2.23 inference(fool_elimination,[],[f203])). 13.62/2.23 thf(f203,plain,( 13.62/2.23 (c_False = ! [X0 : $o] : X0)), 13.62/2.23 inference(rectify,[],[f60])). 13.62/2.23 thf(f60,axiom,( 13.62/2.23 (c_False = ! [X0 : $o] : X0)), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11)). 13.62/2.23 thf(f367,plain,( 13.62/2.23 (c_not = ((cCOMB @ vIMP) @ c_False))), 13.62/2.23 inference(cnf_transformation,[],[f255])). 13.62/2.23 thf(f255,plain,( 13.62/2.23 (c_not = ((cCOMB @ vIMP) @ c_False))), 13.62/2.23 inference(fool_elimination,[],[f254])). 13.62/2.23 thf(f254,plain,( 13.62/2.23 (c_not = (^[X0 : $o] : (X0 => c_False)))), 13.62/2.23 inference(rectify,[],[f35])). 13.62/2.23 thf(f35,axiom,( 13.62/2.23 (c_not = (^[X0 : $o] : (X0 => c_False)))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13)). 13.62/2.23 thf(f322,plain,( 13.62/2.23 ($true = (c_not @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))))), 13.62/2.23 inference(cnf_transformation,[],[f287])). 13.62/2.23 thf(f287,plain,( 13.62/2.23 ($true = (c_not @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))))), 13.62/2.23 inference(fool_elimination,[],[f286])). 13.62/2.23 thf(f286,plain,( 13.62/2.23 (c_not @ ? [X0] : ((c_In @ X0) @ c_Empty))), 13.62/2.23 inference(rectify,[],[f61])). 13.62/2.23 thf(f61,axiom,( 13.62/2.23 (c_not @ ? [X0] : ((c_In @ X0) @ c_Empty))), 13.62/2.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)). 13.62/2.23 % SZS output end Proof for theBenchmark 13.62/2.23 % (6365)------------------------------ 13.62/2.23 % (6365)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 13.62/2.23 % (6365)Termination reason: Refutation 13.62/2.23 13.62/2.23 % (6365)Memory used [KB]: 18933 13.62/2.23 % (6365)Time elapsed: 1.628 s 13.62/2.23 % (6365)------------------------------ 13.62/2.23 % (6365)------------------------------ 13.62/2.23 % (6338)Success in time 1.877 s 13.62/2.23 EOF